The equation t = C + S tan φ (shear strength = cohesion + normal stress × tan φ) is given by:
Try it first: pick an option, then read the explanation.
Correct answer: B. Coulomb
Asked in SSC JE 2009
Detailed Explanation
In 1776, Charles-Augustin de Coulomb, working on earth pressure behind retaining walls, proposed that the shear strength of soil has two parts: cohesion and friction proportional to normal stress.
Why “Coulomb” Is Correct
This is Coulomb's equation, τ = c + σ tan φ. Mohr later (1900) showed how failure depends on the combination of stresses, and the two ideas together form the Mohr–Coulomb criterion.
Why the Other Options Are Wrong
- A. Rankine: Rankine developed an earth pressure theory (1857), not the strength equation.
- C. Newton: Newton's law of viscosity relates shear stress to velocity gradient in fluids.
- D. Mohr: Mohr gave the failure theory using stress circles; the linear equation is Coulomb's.
Key Point
Coulomb: the equation. Mohr: the circles. Together: Mohr–Coulomb.
Key Concepts for Students
- Terzaghi later rewrote it in effective stress: τ = c′ + σ′ tan φ′.
- Coulomb's wedge theory of earth pressure uses the same friction idea.
- In this equation S stands for normal stress σ, and t for shear strength τ.
Practice more: this is question 45 in Shear Strength of Soils MCQs – Part 3. Try the whole set and check every answer instantly.